Bearing Capacity of Strip Footing on Sand Layer … · Bearing Capacity of Strip Footing on Sand Layer Underlain by Rockbase of Different Topography ... Brown and Meyerhof (1969),

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Bearing Capacity of Strip Footing on Sand Layer Underlain by

Rockbase of Different Topography

هقدم هن

م. أيون حودى هطز

هاجستيز هيكانيكا التزبة وهندسة األساسات

[email protected]

قسن العلىم الهندسية والفنىن التطبيقية

سخانيىن –كلية العلىم والتكنىلىجيا

م. هنذر أحود قاسن

هاجستيز هيكانيكا التزبة وهندسة األساسات

[email protected]

قسن العلىم الهندسية والفنىن التطبيقية

خانيىنس -كلية العلىم والتكنىلىجيا

هقدم الى

الوـؤتـوـز العلـوـى األول

دور الكليات والجاهعات فى تنوية الوجتوع

23/10/2013

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Abstract

The current paper studies the bearing capacity of strip footings

resting a sand layer under by a rock stratum. The rock topography is

considered to be the junction between a horizontal surface and an inclined

surface coinciding under the footing.

A numerical parametric study is performed examine the relation

between the different geometric and stiffness parameters and the bearing

capacity of the footing. Sand layer stiffness is represented by its ratio to the

underlying rock stiffness (Er) and its angle of shear resistance (). Sand

layer topology is defined by its thickness (D), relative distance of rock crest

to the center of footing (X) and the slope of the underlying rock layer ().

Results obtained in this paper confirmed the sensitivity of the bearing

capacity to all the topology mentioned earlier. It also should that for weak

rocks-cement sand with (Er) larger than 40% show negligible effect of the

bearing capacity ratio.

Key words: bearing capacity, layered soils, numerical analysis.

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الممخص

لحالى بدراسة األساسات الشريطية المرتكزة عمى طبقة سطحية من الرمل والتى يختص البحث ا

، تتغير طبوغرافيا الطبقة الصخرية من السطح األفقى الى السطح ترتكز بدورىا عمى قاعدة صخرية

وقد تم التركيز عمى ىذا الموضوع نظرا لعدم توافر ما يكفى من األبحاث فى ىذا المائل تحت القاعدة.

. المجال

، حيث قسمت المتغيرات تم دراسة المتغيرات المؤثرة فى ىذه المشكمة بطريقة التحميل العددى

األول يتمثل فى خصائص التربة والثانى يمثل األبعاد اليندسية لمقاعدة والتربة المؤثرة الى قسمين

لرمل والقاعدة أسفميا. درست خصائص التربة من خالل معامل المرونة الممثل بالصالبة النسبية بين ا

(. األبعاد اليندسية لمقاعدة والتربة )وزاوية االحتكاك لمتربة (Erالصخرية والتى يرمز لو بالرمز )

(، مكان األساس Dأسفميا قدمت بالمتغيرات الثالثة, سمك الطبقة الرممية والذى يرمز لو بالرمز )

(.بالزاوية ) (، ميل الطبقة الصخرية والذى يرمز لوXوالذى يرمز لو بالرمز )

أكدت النتائج بشكل عام أن مقاومة االرتكاز لألساسات الشريطية تتأثر بشكل واضح بالعوامل

المذكورة أعاله طالما كان سمك طبقة الرمل صغيرا بالمقارنة بعرض األساس، وكذلك يقل التأثر بيذه

العوامل كمما زادت الصالبة النسبية بين طبقة الرمل و الصخر.

قدرة تحمل التربة، التتابع الطبقى، التحميل العددى. :االفتتاحيةالكممات

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Introduction

The ultimate bearing capacity of shallow foundation is one of the major

geotechnical engineering problems, that highly governed by the nonhomogenity

of the bearing strata. The nonhomogenity may resulted from many

configurations; one of them is the stratified composition of the soil deposit.

Two-layer system was, and still, the field of numerous researches such as

Button (1953), Siva Reedy and Sirnivasan (1967), James et al (1969), Abdrabbo

and Mahmoud (1989) and Keny and Andrawes (1995). The relative rigidity

between the two layers was the most important factor, or almost the unique

factor, around which the previous studies were focusing such as Techeng

(1957), Brown and Meyerhof (1969), Meyerhof (1974), Meyerhof and Hanna

(1978), Hanna and Meyerhof (1980), Michalowski and Lei shi (1995), Merifield

(1999), Yin, Wang and Selvadurai (2001), Zhu, Lee and Jiang (2001) and Brad

Carter (2005).

The survey of the available literature indicated that there is a shortage and

information lag about the case of two-layer system composed of soil layer

overlying a rock base. A limited number of researches were concerning with the

case of a horizontal surface of the rock base such as Mandel and Salencon

(1969) and Cerato and Lutenegger (2006). Different topographies for the

surface of the rock base were not the subjects of the recently available

researches. The current paper is focusing on the effect of the rock surface

topography on the bearing capacity of shallow rigid strip footings. An inclined

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rock surface was the considered, in which the surface was horizontal and at a

given crest, the surface was suddenly inclined to angle () with the horizontal.

Numerical parametric study was performed by using the finite element program

“PLAXIS”, (version 8.2).

The soil layer was considered as sand of variable unit weight () and

corresponding angle of internal friction (). The variation of sand properties

enabled the consideration of different values of the compression modulus (E).

The compression modulus of sand was normalized by the compression modulus

of rock via the ratio (Er), named Relative Rigidity of sand/rock system. The

variation of (Er) indicated the effect of sand properties on the bearing capacity

of strip footings. The geometry of the system was presented by the depth of

sand layer (D), the location of the footing center relative to the crest point (X),

the inclination angle of rock surface (), and the relative rigidity (Er). The

dimensions (D) and (X) were normalized by the footing width (B), as ratios

(D/B) and (X/B), respectively. Wide ranges for the abovementioned factors

were considered to investigate their effects on the bearing capacity of the strip

footings.

The analysis of the obtained results indicated that the bearing capacity

value was very sensitive to the system geometry in which the rock surface

topography was considered the most important factor. The effect of relative

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rigidity of the soil/rock system on the bearing capacity of strip footing is

relatively obvious.

System Definition

The study aims to evaluate the bearing capacity of a shallow strip footing,

subjected to vertical concentric load and resting on nonhomogeneous soil strata.

The strata are composed of a top sand layer followed by a layer of rock of

infinite depth. The top surface of rock is suddenly changed from a horizontal

plane to inclined plane at a specified crest, as shown in figure. The horizontal

part of the rock surface is at a depth (D) below the foundation level. At the

crest, the rock surface is inclined with an angle () to the horizontal. The

location of the strip footing was related to the crest of the rock surface. A

distance (X) was used to define the location of the footing center right or left to

the crest according to the sign convention shown in Figure 1.

Figure 1 System Definition

Parametric Study

In the performed parametric study, the soil properties and the geometry of

the system are presented by different variables as follows:

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Soil Properties

The soil properties are presented via the relative rigidity (Er) that relate

the modulus of elasticity of soil (E1) to the modulus of elasticity of rock (E2),

as; ModulusRockE

ModulusSoilEEr

2

1 .

The soil modulus is chosen according to the considered unit weight () and the

corresponding angle of internal friction (). Consequently, the value of (E1) and

interns the value of (Er) were changed according to the value of () and (),

presented the range of variation of the relative rigidity (Er) and the

corresponding variation of the angle of internal friction () and variation of unit

weight ().

Table 1Considered Range of Soil Properties, E2 = 250 Mpa, as a constant

Relative Rigidity,

2

1

E

EEr

5% 10% 15% 40%

Angle of internal fiction, () 30o 32

o 35

o 40

o

Unit weight, (), (kN/m3) 17 18 19 20

Problem Geometry

The geometry of the system is presented through different variables such as;

Soil depth to footing width ratio, (D/B). The values of (D/B) are selected

to be 0.25, 0.5, 1.0 and 2.0.

Footing location to footing width ratio, (X/B). The analysis is considered

at (X/B) equal -4.0, -2.0, -1.0, -0.5, 0.0, +0.5, +1.0, +2.0 and +4.0.

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Rock surface inclination angle, (). The values of () are varied from

zero to 60o with an interval of 15

o.

It is worth to mention that the presented ranges of geometry are considered for

each case of soil properties presented in Table 1.

Results and Discussions

For each case of loading, the ultimate bearing capacity was recorded and

normalized by the ultimate bearing capacity of a reference case. The reference

case was the case of strip footing under concentric vertical load resting at the

free surface of a homogeneous sand deposit. The normalization was presented

by the Bearing Capacity Ratio (BCR) which is:

CasereferencetheofCapacityBearingUltimate

CaseanyofCapacityBearingUltimateBCR

The effects of soil properties and geometry on values of BCR are

investigated and the subsequent sections present the effect of each parameter.

Effect of Soil Thickness

As presented and obvious through Figure 2 to Figure 6, the bearing capacity

ratio (BCR) is generally decreased with the increase of the soil thickness ratio

(D/B). This trend is existing regardingless to the soil rigidity (Er) or the other

system geometry factors ( and X/B). These results confirmed that the effect of

the rock base on the bearing capacity of the strip footing was vanished

once 00.1/ BD .

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a

= 0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

D/B

BCR

Er = 5%

Er = 10%

Er = 15%

Er = 40%

Figure 2 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with ()

b

= 15o

X/B = 0.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

D/B

BCR

Er = 5%

Er = 10%

Er = 15%

Er = 40%

Figure 3 Effect of (D/B) on the Bearing Capacity

Ratio (BCR) at different values of (Er), with

()

c

= 30o

X/B = 0.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

D/B

BCR

Er = 5%

Er = 10%

Er = 15%

Er = 40%



()

d

= 45o

X/B = 0.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

D/B

BCR

Er = 5%

Er = 10%

Er = 15%

Er = 40%



()

e

= 60o

X/B = 0.0

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

D/B

BCR

Er = 5%

Er = 10%

Er = 15%

Er = 40%



()

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Effect of Footing Location

According to the sign convention of the footing location coordinate (X), the

footing at negative coordinates was completely above the horizontal surface of

the rock base whereas, at positive coordinate it was completely above the

inclined surface of the rock base.

As a general observation, through Figure 7 to Figure 10, by moving the

footing far from the origin in negative direction of (X) the BCR is increased and

vice verse, the BCR is decreased by moving the footing in positive direction.

The effect of rock surface slope is decreased by moving either positively

or negatively along the (x) axis. In positive direction, the effect of rock surface

is vanished and the BCR decreased to 1.00, i.e. the bearing capacity is similar to

that of homogeneous bed of sand. On the other hand, in negative direction, the

bearing capacity increased to reach the value of a sand layer resting on a

horizontal bed of rock (=0).

Accordingly the effect of soil depth ratio (D/B) is controlling the BCR as

long as the footing was moving along the negative direction of (x) axis. The

comparison between the Figure 7 to Figure 10, can confirmed, as mentioned

before, that the sensitivity of the BCR to the variation of (X/B) is decreased

with the increase the relative rigidity (Er). Finally, as obvious in the figures,

satisfying two conditions, or even only one of them, is enough to vanish the

effect of the footing location ratio (X/B). One of these conditions is the

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increasing of the soil depth to be 00.1/ BD , whereas the other one is the

increasing of the soil rigidity to be %40rE .

a

= 15o

Er = 5 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR

D/B=0.25

D/B=0.50

D/B=1.00

D/B=2.00

Figure 7 Effect of (X/B) on the Bearing Capacity

Ratio (BCR) at different values of (D/B), with

(Er=5%)

b

= 15o

Er = 10 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR

D/B=0.25

D/B=0.50

D/B=1.00

D/B=2.00



(Er=10%)

c

= 15o

Er = 15 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR

D/B=0.25

D/B=0.50

D/B=1.00

D/B=2.00



(Er=15%)

d

= 15o

Er = 40 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR

D/B=0.25

D/B=0.50

D/B=1.00

D/B=2.00



(Er=40%)

Effect of Inclination angle of Rock Surface ()

In order to investigate the effect of the sudden change of rock surface into

different inclination angles, the relationships between (BCR) and footing

location ratio (X/B) were drawn for a range of () from = 0 to = 60o. These

relationships are shown in Figure 11 to Figure 14, at given values of (D/B),

chosen as 0.25, with different values of (Er).

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As shown in Figure 11 to Figure 14, the general trend of the obtained

relationships is, as long as the footing is moving from the far location in

negative direction towards the crest or the point of change, the (BCR) was

gradually decreased, to be 1.00 at the far location in positive direction. This

behavior was discussed in the last section, so that it was not the objective of

Figure 11 to Figure 14.

The objective of Figure 11 to Figure 14 was presenting how the rate of

the decrement in (BCR) was highly affected by the inclination angle (). It is

obvious that the rate of reduction is increased with the increase of the angle ().

The largest effect is obtained once the center line of the footing is passing the

crest, i.e. at the location ratio (X/B = 0). It is worth to mention here, that all the

sensitivity of the (BCR) to the inclination angle (), as one of the system

geometry factors, is decreased to be vanished at the rigid soil of Er=40%.

a D/B = 0.25

Er = 5 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR

Figure 11 Effect of footing location ratio (X/B) on

the (BCR) at different values of (), with (Er=5%)

b D/B = 0.25

Er = 10 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR


the (BCR) at different values of (), with (Er=10%)

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c D/B = 0.25

Er = 15 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR


the (BCR) at different values of (), with

(Er=15%)

d D/B = 0.25

Er = 40 %

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-4 -3 -2 -1 0 1 2 3 4

X/B

BCR


the (BCR) at different values of (), with

(Er=40%)

Effect of Relative Rigidity, (Er)

In order to investigate the effect of relative rigidity (Er), the relationships

between (BCR) and footing depth ratio (D/B) were drawn for a range of (Er)

from Er = Rigid Base, 1%, 5%, as shown in Table 2. These relationships, as

shown in Figure 15 to Figure 17, were drawn at given values of (), chosen as

(=0.0), with different values of surcharge ratio (Rq).

Besides the numerical range of (Er), Mandel and Salencon‟s (1969)

theory added to the figures as the theoretical solutions.

As shown in Figure 15 to Figure 17, the bearing capacity ratio (BCR) was

generally decreased with the increase of the soil thickness ratio (D/B). Besides

this general remark, the (BCR) was founded to be sensitive to the relative

rigidity (Er), as shown in the collected Figure 15 to Figure 17, the (BCR) is

generally increased with the increase of relative rigidity (Er).

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The objective of Figure 15 to Figure 17 is comparing the numerical

solutions and the theoretical solutions. The theoretical result is similar to the

result from numerical solution when the relative rigidity is equal rigid base.

It is obvious that the (BCR) in the theoretical solutions depend on the

higher relative rigidity, (Er=Rigid Base). But the (BCR) in the numerical

solutions depend on the relative rigidity where the (BCR) increased with the

increase the relative rigidity.

Table 2 Considered Range of Relative Rigidity

Relative Rigidity,

2

1

E

EEr

(Rigid

Base)

1% 5%

E2, (MPa) 1250 250

E1 = 12500 KPa, as a constant.

a

Rq=0.00B

=0.0

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

D/B

BCR

Mandel &

Salencon (1969)Rigid Base

Er=1%

Er=5%

Figure 15 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er),with

(Rq=0.00B)

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b

Rq=0.50B

=0.0

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

D/B

BCR

Mandel &


Er=1%

Er=5%


Ratio (BCR) at different values of (Er),with

(Rq=0.50B)

c

Rq=1.00B

=0.0

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

D/B

BCR

Mandel &


Er=1%

Er=5%


Ratio (BCR) at different values of (Er),with

(Rq=1.00B)

Conclusions

The study aims to focus on the bearing capacity of a shallow strip footing,

subjected to vertical concentric load and resting on nonhomogeneous soil strata.

The strata were composed of a top sand layer followed by a rock bed of infinite

extent. The upper surface of rock was considered have a suddenly change from

a horizontal plane to inclined plane at a specified crest.

The ultimate bearing capacity was estimated to explain how it may affect

by different factors such as the relative rigidity of soil (Er), the system such as

depth (D), location of footing (X), inclination angle ().

A parametric study was carried out using a finite element method via the

well established program PLAXIS, which is intended for the analysis of

deformation and stability in geotechnical engineering projects. The parametric

study revealed the following conclusions:

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The bearing capacity ratio (BCR) of single strip footing was generally

decreased with the increase of the soil thickness ratio (D/B).

The effect of the rock base on the bearing capacity of the strip footing was

vanished once 00.1/ BD .

If the strip footing is constructed far from the origin in negative direction of

(X) the BCR was increased and vice versa, the BCR was decreased by

moving the footing in positive direction.

Increasing the soil depth ratio 00.1/ BD and/or increasing the soil rigidity

%40rE were enough to vanish the effect of footing location ratio (X/B)

on the value (BCR).

BCR generally was decreased with the increase of the inclination angle of

rock surface () for the soil having the same value of relative rigidity (Er)

and the same location of footing (X).

The effect of the inclination angle of rock surface () is affected by moving

the footing either positively or negatively along the (x) axis. In positive

direction, the effect of the inclination angle of rock surface () is vanished

and the BCR decreased to 1.00, i.e. the bearing capacity is similar to that of

homogeneous bed of sand. On the other hand, in negative direction, the

bearing capacity increased to reach the value of a sand layer resting on a

horizontal bed of rock (=0).

17

The largest affect of the inclination angle of rock surface () is obtained

once the center line of the strip footing is passing the crest, i.e. at the location

ratio (X/B=0.0).

Increasing the soil rigidity %40rE were enough to vanish the effect of

inclination angle of rock surface ().

The (BCR) in the theoretical solutions, (Mandel and Salencon‟s (1969)),

depend on the higher relative rigidity, (Er=Rigid Base). But the (BCR) in the

numerical solutions depend on the relative rigidity where the (BCR)

increased with the increase the relative rigidity.

The results from the numerical solutions approved an agreement with the

results from the theoretical solutions such as Mandel and Salencon‟s (1969)

at (Er=Rigid Base).

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References

[1] Button, S. J. (1953). “The Bearing Capacity of Footings on Two-Layer Cohesive

Subsoil”, Proceedings, 7th

International Conference on Soil Mechanics and

Foundation Engineering, Zurich, vol1, pp. 332-335.

[2] Reddy, A.S. and Srinivasan, R.J., (1967). “Bearing Capacity of Footings on Layered

Clays”, Journal of the Soil Mechanics and Foundations Division, ASCE, 93, SM2, pp.

83-99.

[3] James, C.H.C., Krizek, R.J., and Baker, W.H., (1969). “Bearing Capacity of Purely

Cohesive Soils with a nonhomogeneous Strength Distribution”, Highway Research

Record, No. 282, pp. 48-56.

[4] Abdrabbo, F. M., and Mahmoud, M. A. (1989). “Bearing Capacity of Shallow

Footing on Sand bed intervened by a Clay Layer”, Al-Azhar engineering first

conference.

[5] Kenny, M. J., and Andrawes, K. Z., (1995).” Technical note, „The Bearing Capacity

of Footings on Sand Layer overlying Soft Clay”, Geotechnique 47, No. 2, 339-345.

[6] Tcheng, Y., (1957). “Shallow Foundations on a Stratified Soil”, Proc. 4th ICSMFE,

London, Vol. 1, pp. 449-452.

[7] Brown, J.D., and Meyerhof, G.G., (1969). “An Experimental Study of the Ultimate

Bearing Capacity of Layered Clay Foundations”, Seventh International Conference on

Soil Mechanics and Foundation Engineering, 2: 45-51.

[8] Meyerhof, G.G., (1974). “Ultimate Bearing Capacity of Footing on Sand Layer

Overlying Clay”, Canadian Geotchnical Journal, Vol. 11, pp. 223-229.

[9] Meyerhof, G. G, and Hanna, A. M. (1978). “Ultimate bearing capacity of foundations

on layered soils under inclined load”, Canadian Geotechnical Journal, 15, pp. 565-

572.

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[10] Hanna, A. M., and Meyerhof, G. G. (1980). “Design Charts for Ultimate

Bearing Capacity of Foundations on Sand overlying Soft Clay”. Canadian

Geotechnical Journal, 17: 300–303.

[11] Michalowski, R. L., and Shi, L. (1995). “Bearing Capacity of Footings over

Two-Layer Foundation Soils”, J. of Geotech. Engineering. ASCE, 121(5), 421–428.

[12] Merifield, R. S., Sloan, S. W. & Yu, H. S. (1999). “Rigorous Plasticity

Solutions for the Bearing cCapacity of Two-Layered Clays”, Geotechnique 49, No. 4,

471-490.

[13] Jian-Hua Yin, Yu-Jie Wang, and A. P. S. Selvadurai. (2001). “Influence of

nonassociativity on the bearing capacity of a strip footing”, Journal of Geotechnical

and Geoenvironmental Engineering, Vol. 127, No. 11, pp. 985-989.

[14] Zhu, D.Y., Lee, C.F. & Jiang, H.D., (2001). “A numerical Study of the

Bearing Capacity Factor N”, Canadian Geotchnical Journal, Vol. 38, pp.1090–1096.

[15] Brad Carter, (2005). “Bearing Capacity of a Strip Footing on a Layered Soil”

Senior Report, CE 5943, University of New Brunswick.

[16] Mandel, J., and Salencon, J., (1969). “Force portante d‟un sol sur une assise

rigide”, In Proc., VII Int. Conf. Soil Mechanics Foundation Engineering., Mexico

City, 2, pp. 157.

[17] Cerato, A. B. and Lutenegger, A. J. (2006). “Technical Note, Bearing

Capacity of Square and Circular Footings on a Finite Layer of Granular Soil

Underlain By A Rigid Base”, Journal of Geotechnical and Geoenvironmental

Engineering, Vol. 132, No. 11, ASCE, pp. 1496-1501.

20

List of Symbols

B Width of footing

BCR Bearing capacity ratio

D Depth of sand layer

E1 Young‟s modulus of elasticity of soil

E2 Young‟s modulus of elasticity of rock

Er Relative rigidity

X Location of footing

Rock inclination angle

Angle of internal friction of soil

Unit weight of soil

LIST OF FIGURES

Figure 1 System Definition ........................................................................................................ 6

Figure 2 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of (Er), with

() .......................................................................................................................................... 9


() ....................................................................................................................................... 9


() ....................................................................................................................................... 9


() ....................................................................................................................................... 9


() ....................................................................................................................................... 9

Figure 7 Effect of (X/B) on the Bearing Capacity Ratio (BCR) at different values of (D/B),

with (Er=5%) ............................................................................................................................ 11

21


with (Er=10%) .......................................................................................................................... 11


with (Er=15%) .......................................................................................................................... 11


with (Er=40%) .......................................................................................................................... 11

Figure 11 Effect of footing location ratio (X/B) on the (BCR) at different values of (), with

(Er=5%) .................................................................................................................................... 12


(Er=10%) .................................................................................................................................. 12


(Er=15%) .................................................................................................................................. 13


(Er=40%) .................................................................................................................................. 13

Figure 15 Effect of (D/B) on the Bearing Capacity Ratio (BCR) at different values of

(Er),with (Rq=0.00B) ............................................................................................................. 14


(Er),with (Rq=0.50B) .............................................................................................................. 15


(Er),with (Rq=1.00B) .............................................................................................................. 15

LIST OF TABLES

Table 1Considered Range of Soil Properties, E2 = 250 Mpa, as a constant .............................. 7

Table 2 Considered Range of Relative Rigidity ...................................................................... 14

Documents

Bearing Capacity of Strip Footing on Sand Layer … · Bearing Capacity of Strip Footing on Sand Layer Underlain by Rockbase of Different Topography ... Brown and Meyerhof (1969),